Marketing surveys conducted by the sales manager for a company determined that 3,000 power drills could be sold for $70 each, but 4,000 drills could be sold for $60 each.
(a)
If the two data points were plotted on a coordinate system with the number of drills sold on the horizontal axis and the price of each drill on the vertical axis, what is the slope of the line between the two points?
(b)
Write a sentence that explains the result in part (a) in the context of this problem.
For every additional drill sold, the price per drill (in cents) decreases by ? cent(s).
(c)
Assuming the trend in part (a) continues, how many drills can be sold for $63?
(a) The slope of the line between the two points can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Where:
x1 = 3000 drills sold
y1 = $70 per drill
x2 = 4000 drills sold
y2 = $60 per drill
Plug in the values:
slope = ($60 - $70) / (4000 - 3000)
slope = (-$10) / 1000
slope = -0.01
So, the slope of the line between the two points is -0.01.
(b) For every additional drill sold, the price per drill decreases by 1 cent.
(c) To find out how many drills can be sold for $63, we can set up an equation using the slope:
($63 - $70) = -0.01 * (x - 3000)
Simplify the equation:
-$7 = -0.01x + 30
-$37 = -0.01x
x = 3700
Therefore, 3,700 drills can be sold for $63.